Corresponding Angles Postulate and Consecutive Interior Angles Theorem

Kathleen D., Miranda J., Danielle C., and Rachel S.

Corresponding Angles Postulate:

Corresponding Angles Postulate-
states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent.

Examples:


Name four corresponding angles.

Answers: <3 and <7
<2 and <6
<4 and <8
<1 and <5

Consecutive Interior Angles Theorem:

Definition of Consecutive Interior Angles: If two lines are cut by a transversal, Then the pairs of angles inside the two lines are called Consecutive Interior Angles.

Consecutive Interior Angles Theorem:
If two parallel lines are cut by a transversal, then the pairs of consecutive interior anglers formed are supplementary.

To help you remember: the angle pairs are "Consecutive" (they follow each other), and they are on the "Interior" of the two crossed lines


Identifying Consecutive Interior Angles:

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.

Consecutive Interior Angles

Consecutive Interior Angles are formed when two parallel lines are cut by a transversal.

In the figure, angles 3 and 5 are consecutive interior angles.
Also angles 4 and 6 are consecutive interior angles.


Proof:
Given: k || l is a transversal
Prove: are supplementary and are supplementary.

	Statement	Reason
1	k	l, t is a traversal.	Given
2	form a linear pair and form a linear pair.
3	are supplementary are supplementary.
4
5	are supplementary are supplementary.

Answer:


Proof:
Given: k || l is a transversal
Prove: are supplementary and are supplementary.

	Statement	Reason
1	k	l, t is a traversal.	Given
2	form a linear pair and form a linear pair.	Definition of linear pair
3	are supplementary are supplementary.	Supplement postulate
4		Alternate Interior Angle Theorem
5	are supplementary are supplementary.	Substitution Property

Determine whether the pairs of angles are Consecutive Interior Angles or not:
1) <3 and <5
2) <7 and <2
3) <8 and <1
4) <6 and <3
5) <6 and <4



Answers:
1) Yes
2) No
3) No
4) No
5) Yes